Developing statistical methodologies for Anthropometry · 2013-09-02 · Developing statistical methodologies for Anthropometry Guillermo Vinu e Visus PhD Student Faculty of Mathematics

Developing statistical methodologies forAnthropometry

Guillermo Vinue VisusPhD Student

Faculty of MathematicsUniversity of Valencia, Spain

Jointly with Guillermo Ayala Gallego, Juan Domingo Esteve, Esther DuraMartınez (University of Valencia), Amelia Simo Vidal, Marıa Victoria

Ibanez Gual, Irene Epifanio Lopez (University Jaume I of Castellon) andSandra Alemany Mut (Biomechanics Institute of Valencia)

18th European Young Statisticians Meeting, 26-30 August 2013, Osijek,Croatia

Motivation and problematicSpanish anthropometric survey

Statistical approachesConclusions

Basic references

Outline

1 Motivation and problematic

2 Spanish anthropometric surveyAnthropometric databaseLandmarks

3 Statistical approachesClothing development processHuman modellingR package

4 Conclusions

5 Basic references

Guillermo Vinue Visus Developing statistical methodologies for Anthropometry 2/30



Basic references

Motivation and problematic

Clothing development process and human modelling require updatedanthropometric data to develop new patterns.

Body measurements have been traditionally taken by using rudimentarymethods.

* Advantages:

- Procedures are very easy to use.- No particularly expensive.

* Drawbacks:

- The shape information is imprecise and inaccuracy.- Interaction with real subjects.

New 3D body scanner technologies constitute a step forward in the wayof collecting anthropometric data.

Anthropometric surveys in different countries (Spain, 2006).




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Anthropometric databaseLandmarks

Anthropometric database

A national 3D anthropometric survey of the female population wasconducted in Spain in 2006 by the Spanish Ministry of Health.

Aim: To generate anthropometric data from the female populationaddressed to the clothing industry.

Database: Sample of 10.415 Spanish women randomly selected:

* From 12 to 70 years old.* 95 anthropometric measurements.* 66 points representing their shape.* Socio-demographic survey.




Basic references

Anthropometric databaseLandmarks

Landmarks

The shape of all the women of the database is represented by landmarks.

Landmark: Point (x , y , z) of correspondence on each individual thatmatches between and within populations.

The configuration is the set of landmarks ⇒ X ∈M66×3(R)

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Landmark Description

1. Head back Most prominent point of the head in the sagital plane2. Head front Glabela (most promininet point of the forehead)3. Forearm wrist left Maximum girth of the left forearm4. Forearm girth left Maximum girth of the left forearm just under the left elbow5. Forearm wrist right Maximum girth of the right forearm..... .....66. Left iliac crest Physical marker on the left of the iliac crest




Basic references

Clothing development processHuman modellingR package

Statistical approaches

Clothing development processClustering:

* Trimmed PAM.* Hierarchical PAM.

Statistical shape analysis:

* k-means adapted.

Human modelling

Archetypal analysis:

* Archetypes & Archetypoids.

R package




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Clothing development process




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Clothing development process (I)

Clothing development process: To define a sizing system that fits good.

Current sizing systems don’t cover all morphologies.

Causes:

* Old size charts.* Clothing manufacturers work by trial and error.* Sizing systems are not standardized.

The final evaluation of fit needs fit models.

A good fit model is the basis for defining an accurate sizing system.

They define a single fit model for the whole target market.

There is not much information to help choose a fit model.




Basic references


Clothing development process (II)

Consequences: Lack of fitting of the sizing systems.

* Large amount of unsold garments (company competitivity loss).* High index of returned garments (customer dissatisfaction).

Proposals in the literature to define sizing systems:

* Multivariate approaches (PCA, Clustering).* Optimization algorithms (McCulloch et al. (1998)).

Proposals in the literature to define fit models:

* There are not any statistical method aimed at defining fit models.

Our proposals:

* Sizing system:

- Trimmed PAM.- k-means in the shape space.

* Fit models: Hierarchical PAM.




Basic references


Clustering: Trimmed PAM

Our proposal is an improvement of the work of McCulloch et al. (1998):

* k-medoids clustering method → prototypes will be real persons.* Trimmed k-medoids to leave out outlier individuals.* Extension of the dissimilarity used by McCulloch et al. (1998), dMO .* OWA operators to take into account to the user.

Data set (6013 women and 5 dimensions):

* Not pregnant women. ; Not breast feeding at the time of the survey.* No cosmetic surgery. ; Between 20 and 65 years.* Bust, chest, waist and hip circumference and neck to ground length.

Procedure:

* The data set is segmented in 12 bust classes (EN 13402-2).* The trimmed k-medoids is applied to each segment with k = 3.

Conclusions of this work:

* Assignment of individuals to size.* Derivation of realistic prototypes.* Selection of individual discommodities.




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Apparel sizing using trimmed PAM and OWA operators

M.V. Ibáñez a,⇑, G. Vinué b, S. Alemany c, A. Simó a, I. Epifanio a, J. Domingo d, G. Ayala b

a Department of Mathematics, Universitat Jaume I, Castellón, Spainb Department of Statistics and O.R., University of Valencia, Valencia, Spainc Biomechanics Institute of Valencia, Universidad Politécnica de Valencia, Valencia, Spaind Department of Informatics, University of Valencia, Valencia, Spain

a r t i c l e i n f o

Keywords:Anthropometric dataSizing systemsTrimmed k-medoidsOWA operators

a b s t r a c t

This paper is concerned with apparel sizing system design. One of the most important issues in the appa-rel development process is to define a sizing system that provides a good fit to the majority of the pop-ulation. A sizing system classifies a specific population into homogeneous subgroups based on some keybody dimensions. Standard sizing systems range linearly from very small to very large. However, anthro-pometric measures do not grow linearly with size, so they can not accommodate all body types. It isimportant to determine each class in the sizing system based on a real prototype that is as representativeas possible of each class. In this paper we propose a methodology to develop an efficient apparel sizingsystem based on clustering techniques jointly with OWA operators. Our approach is a natural extensionand improvement of the methodology proposed by McCulloch, Paal, and Ashdown (1998), and we applyit to the anthropometric database obtained from a anthropometric survey of the Spanish female popula-tion, performed during 2006.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The development of ready to wear (RTW) cloth requires an esti-mation of body measures of the target population to generate siz-ing charts, patterns on a basic size and grading parameters.However, most apparel manufacturers create and adjust theirown size charts by trial and error using small customer surveys,mainly models representing the basic size, plus analysis of salesand returned merchandising reports (Chen et al., 2009b). Never-theless, the growing relocation of the pattern and production activ-ities and the poor level of application of sizing standards areproducing one of the main clothing complaints: the lack of fitting.

There are several local and international standards proposing aregulation of the sizing system based on key anthropometricmeasures, but the lack of common rules and criteria is one of thedrawbacks for their implementation. In this context, ’vanity sizing’grows as a common practice among clothing companies. With thisstrategy, companies often adjust the measurement specificationsfor each size based on a sale strategy designed to make consumers,especially women, feel better about fitting into smaller sizes (Fan,Yu, & Hunter, 2004, 2007), and therefore prompting them to buymore. The method we propose is aimed at helping difficult

customers to find the correct size in different companies. In fact,nowadays, the correct size selection is the main obstacle to largescale online garment sales because it is difficult to find the fit gar-ment from the general size information.

A sizing system classifies a specific population into homoge-neous subgroups based on some key body dimensions (Chunga,Lina, & Wang, 2007). The major dilemma is to decide into howmany size groups should the population be divided, in order tooptimize benefits and user satisfaction. Most of the standard sizingcharts propose sizes based on intervals over just one anthropomet-ric dimension. Current standards consider the low correlation be-tween some key dimensions and use bivariate distributions todefine a sizing chart and cross tabulation to select the sizes cover-ing the highest percentage of population. For lower limb garments,European Committee for Standardization (2002) propose the com-bination of three anthropometric dimensions (waist girth, hip girthand stature) leading to a significant increase of the number of sizes.This decreases the profit for the companies since they have to reor-ganize their production lines and make them more complex. More-over, correlations between anthropometric measures show a greatvariability on body proportion. It is not possible to cover so differ-ent body morphologies with these kind of models. That is why,multivariate approaches have been proposed to develop sizing sys-tems. Principal components are often used to reduce the dimen-sion of anthropometric data sets, and the two first principalcomponents are used to generate bivariate distributions (Chenet al., 2009; Gupta and Gangadhar, 2004; Hsu, 2009a, 2009b; Luxi-mon, Zhang, Luximon, Xiao, 2011; Salusso-Deonier, DeLong,

0957-4174/$ - see front matter � 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.eswa.2012.02.127

⇑ Corresponding author.E-mail addresses: [email protected] (M.V. Ibáñez), [email protected]

(G. Vinué), [email protected] (S. Alemany), [email protected] (A. Simó),[email protected] (I. Epifanio), [email protected] (J. Domingo), [email protected] (G. Ayala).

Expert Systems with Applications 39 (2012) 10512–10520

Contents lists available at SciVerse ScienceDirect

Expert Systems with Applications

journal homepage: www.elsevier .com/locate /eswa




Basic references


Clustering: Hierarchical PAM (HIPAM)

HIPAM algorithm: divisive hierarchical clustering method based on PAM(Wit et al. (2004)).

Two HIPAM algorithms adapted to anthropometric data:

* HIPAMMO : HIPAM + dissimilarity dMO + asw.* HIPAMIMO : HIPAM + dissimilarity dMO + INCA (Irigoien et al. (2008)).

The INCA criterion is used to divide the clusters and as a stopping rule.

Data set and procedure:

* Same data set used with by the trimmed PAM procedure.* The data set is also segmented in 12 bust classes (EN 13402-2).* Both HIPAM algorithms are applied to each segment.


* Robust statistical tool to determine accurate fit models.* Automatic detection of outliers.




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Statistical shape analysis

Aim: To use k-means to divide the population according to their shapes.

Fundamental concepts of the statistical shape analysis:

* Pre-shape of an object: It is what is left after allowing for theeffects of translation and scale.

* Shape of an object: It is what is left after allowing for the effects oftranslation, scale, and rotation.

* Procrustes distance, ρ: Closest great circle distance betweenpre-shapes on the pre-shape sphere.

* Procrustes mean: The shape that has the least summed squaredProcrustes distance to all the configurations of a sample.

k-means has been usually applied using a set of anthropometric variablesas input.

k-means: The sample mean is the value that minimizes the Euclideandistance from each point, to the centroid of the cluster to which itbelongs.




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K-means algorithm in the Shape Space

By integrating the Procrustes mean and the Procrustes distance intok-means, we can use it in the shape analysis context.

k-means algorithm to X1, . . . ,Xn configuration matrices:

(i) Given Z = ([Z1], . . . , [Zk ]) [Zi ] ∈ Σ663 i = 1, . . . , k, we minimize with

respect to C = (C1, . . . ,Ck ) assigning each shape ([X1], . . . , [Xn]) to theclass whose centroid has minimum Procrustes distance to it.

(ii) Given C, we minimize with respect to Z , taking Z = ([µ1], . . . , [µk ]),being [µi ] i = 1, . . . , k the Procrustes mean of shapes in Ci .

Steps (i) and (ii) are repeated until convergence of the algorithm.

We adapt the Lloyd k-means unlike Amaral et al. (2010) that useHartigan-Wong k-means.




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K-means algorithm in the Shape Space

Computational statistical tool: R package shapes.

Data set and procedure:

* Same data set used with the trimmed PAM procedure.* We segment our data set using bust and height measurements.* In this way, the size effect is filtered out in an easy way.* We apply the k-means algorithm to each segment (k = 3).

Bust Height1 Height2≤ 162 cm [162− 174[ cm

[74− 82[ cm 240 97[82− 90[ cm 1052 694[90− 98[ cm 1079 671

[98− 106[ cm 772 311[106− 118[ cm 446 170


* k-means adapted in the context of shape analysis to cluster humanbody shapes based on landmarks.

* Lloyd version has better performance than Hartigan-Wong version.




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Clustering results

Bust ∈ [90-98[ ; Height ∈ [162-174[

671 women

Cluster 1 Cluster 2 Cluster 3

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Rotated dataMean shape

Procrustes rotated data for cluster 1 with its mean shape superimposed

Plane xy




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Clustering results

Bust ∈ [90-98[ ; Height ∈ [162-174[

671 women


153 206 312

1 2 3

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Neck to ground

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Plane xy




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Clustering results

Bust ∈ [90-98[ ; Height ∈ [162-174[

671 women


153 206 312

1 2 3

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Neck to ground

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Plane xy




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SECOND REVISION




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Human modelling




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Human modelling

Products intended to fit the users must be designed considering their sizeand shape → Generation of several representative human models.

The human models represent the anthropometric variability of the targetpopulation.

The appropriate selection of this small group is critical.

If the hard to fit extreme individuals are previously identified, the timeand cost of the design process is reduced.

Usual approaches:

* Percentile analysis.* Regression.* PCA.

Our proposal: ARCHETYPAL ANALYSIS (AA) (Cutler et al. (1994)).




Basic references


Archetypal analysis

Let be an n ×m matrix X, multivariate database.

The AA aims at obtaining the n × k matrices α and β which minimize:

RSS =n∑

i=1

‖xi −k∑

j=1

αijzj‖2 =n∑

i=1

‖xi −k∑

j=1

αij

n∑l=1

βjlxl‖2

under the constraints

1)k∑

j=1

αij = 1 with αij ≥ 0 and i = 1, . . . , n

2)n∑

l=1

βjl = 1 with βjl ≥ 0 and j = 1, . . . , k

ARCHETYPE: extreme member of the data set that is a mixture of the

actual data points: zj =n∑

l=1

βjlxl

Archetypes can be computed with the R package archetypes.




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Archetypal analysis vs PCA

Aircraft pilots database from the United States Air Force (USAF) Survey.From the total of variables, we select six (the cockpit dimensions).


* The goal of AA is to obtain extreme individuals.* The level of accommodation is reached with AA.* Archetypes cannot be obtained with PCA.* Number of archetypes is decided either by the user or by a criterion.

Dimension Description

Thumb Tip Reach Measure the distance from thewall to the tip of the thumb.

Buttock-Knee Length Measure the horizontal distancefrom the rearmost surface of theright buttock to the forwardsurface of the right kneecap.

Popliteal Height Sitting Measure the vertical distancefrom the footrest surface to thesuperior margin of the right kneecap.

Sitting Height Measure the vertical distancefrom the sitting surface to thetop of the head.

Eye Height Sitting Measure the vertical distancefrom the sitting surface to theright external canthus (outer“corner” of eye).

Shoulder Height Sitting Measure the vertical distancefrom the sitting surface to theright Acromion - the bony landmarkat the tip of the shoulder.




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Archetypoid analysis

The archetypes do not correspond to observed individuals:

zj =n∑

l=1

βjlxl withn∑

l=1

βjl = 1 and βjl ≥ 0

In some cases it is critical that the archetypes are real subjects.

So far the nearest individuals to archetypes are computed in two ways:

1 nearest: Subjects who have the closest dE to archetypes.2 which: Subjects with the greatest α for each archetype.

The identified archetypes can be artificial: “no economist in our samplefits this archetype to 100%” (Seiler et al. (2013)).

A new archetypal concept is proposed: the ARCHETYPOID:

zj =n∑

l=1

βjlxl withn∑

l=1

βjl = 1 and βjl ∈ {0, 1}

An archetypoid is a real observed individual.

The archetypoids might not be the same as the nearest/which.

The archetypoids always exist even when the features are unavailable.




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0.00

50.

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Aircraft pilots archetypes and archetypoids

Archetypes/Archetypoids

RS

S

1 2 3 4 5 6 7 8 9 10

ArchetypesArchetypoids from nearestArchetypoids from which Aircraft pilots database.

RSS

3 archetypes 0.0123803 archetypoids from which (1632,1822,52) 0.012385

3 archetypoids from nearest (2177,2240,1691) 0.0128which (1421,314,1691) 0.0195nearest (511,314,1691) 0.0182

3 archetypoids (from nearest)

Per

cent

ile

020

4060

8010

0

3 archetypoids (from which)

Per

cent

ile

020

4060

8010

0




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R package




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R package

A new R package calledAnthropometry gatherstogether all thesemethodologies.

Hopefully soon availablefrom CRAN.




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Conclusions

Updated anthropometric data constitute valuable information...

* To optimize sizing systems.* To understand the body shape of the population.* To reduce the design process cycle.

Rigorous statistical methodologies and software tools must be developed.

Our research group has proposed several statistical methods concerningclustering, the statistical shape analysis and the archetypal analysis.

Clustering methodologies and the shape analysis allow...

* To define an optimal clothing sizing system.* To identify the fit models of each size.* To cluster individuals according to their shape.

Methodologies based on the archetypal analysis look for representativesubjects, which help to define coherent human models and mockups.

A new R package has been introduced that joints all these methodologies.




Basic references

Basic references I

Alemany, S., Gonzalez, J. C., Nacher, B., Soriano, C., Arnaiz, C., Heras, H., 2010. Anthropometric survey

of the Spanish female population aimed at the apparel industry. In: Proceedings of the 2010 Intl.Conference on 3D Body scanning Technologies. pp. 307–315.

Amaral, G. J. A., Dore, L. H., Lessa, R. P., Stosic, B., 2010. k-Means Algorithm in Statistical Shape

Analysis. Communications in Statistics - Simulation and Computation 39 (5), 1016–1026.

Claude, J., 2008. Morphometrics with R. Use R! Springer.

Cutler, A., Breiman, L., November 1994. Archetypal Analysis. Technometrics 36 (4), 338–347.

Dryden, I. E., Mardia, K. V., 1998. Statistical Shape Analysis. John Wiley & Sons.

Eugster, M. J., Leisch, F., April 2009. From Spider-Man to Hero - Archetypal Analysis in R. Journal of

Statistical Software 30 (8), 1–23.

European Committee for Standardization, 2002. European Standard EN 13402-2: Size system of clothing.

Primary and secondary dimensions.

Garcıa-Escudero, L. A., Gordaliza, A., Matran, C., Jun. 2003. Trimming tools in exploratory data analysis.

Journal of Computational and Graphical Statistics 12 (2), 434–449.

Georgescu, V., 20th-24th July 2009. Clustering of Fuzzy Shapes by Integrating Procrustean Metrics and Full

Mean Shape Estimation into K-Means Algorithm. In: IFSA-EUSFLAT Conference.




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Basic references II

Irigoien, I., Arenas, C., 2008. INCA: New statistic for estimating the number of clusters and identifying

atypical units. Statistics in Medicine 27, 2948–2973.

Kaufman, L. and Rousseeuw, P.J., 1990. Finding Groups in Data: An Introduction to Cluster Analysis. John

Wiley, New York.

Leon, T., Zuccarello, P., Ayala, G., de Ves, E., Domingo, J., 2007. Applying logistic regression to relevance

feedback in image retrieval systems. Pattern Recognition 40, 2621–2632.

Mardia, K., Kent, J., Bibby, J., 1979. Multivariate Analysis. Academic Press.

McCulloch, C., Paal, B., Ashdown, S., 1998. An optimization approach to apparel sizing. Journal of the

Operational Research Society 49, 492–499.

Pollard, K. S., van der Laan, M. J., 2002. A method to identify significant clusters in gene expression data.

Vol. II of SCI2002 Proceedings. pp. 318–325.

Wit, E., McClure, J., 2004. Statistics for Microarrays: Design, Analysis and Inference. John Wiley & Sons,

Ltd.


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Developing statistical methodologies for Anthropometry · 2013-09-02 · Developing statistical methodologies for Anthropometry Guillermo Vinu e Visus PhD Student Faculty of Mathematics